Quantized multiplicative quiver varieties and actions of higher genus braid groups di Jordan, David Andrew

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Parabolic induction and restriction functors for rational Cherednik algebras di Bezrukavnikov, Roman, Etingof, Pavel I.

“...Parabolic induction and restriction functors play an important role in the representation theory of finite and affine Hecke algebras. This makes it desirable to generalize them to the setting of double affine Hecke algebras, or Cherednik algebras. ...”
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Dirac cohomology of one-W-type representations di Ciubotaru, D, Moy, A

“...Soc. 351 (1999), no. 10, 4245-4261] in the more general setting of modules for graded affine Hecke algebras with parameters. We show that every such one K-type module has nonzero Dirac cohomology (in the sense of [D. ...”

Parabolic Character Sheaves, III di Lusztig, George

“...This has applications to a geometric con- struction of certain affine Hecke algebras with unequal parameters, as will be shown elsewhere....”
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ON THE SATAKE ISOMORPHISM di LUSZTIG, G.

“...Abstract In a 1983 paper, the author has established a (decategorified) Satake equivalence for affine Hecke algebras. In this paper, we give new proofs for some results of that paper, one based on the theory of J-rings and one based on the known character formula for rational representations of a reductive group in positive, large characteristic. ...”
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Symplectic Dirac operators for Lie algebras and graded Hecke algebras di Ciubotaru, D, De Martino, M, Meyer, P

“...We work in the settings of ℤ/2-graded quadratic Lie algebras 𝔤 = 𝔨 + 𝔭 and of graded affine Hecke algebras ℍ. In these contexts, we show analogues of the Parthasarathy’s formula for [D+, D–] and certain generalisations of the Casimir inequality....”

Dirac cohomology for symplectic reflection algebras di Ciubotaru, D

“...We generalize in this way the Dirac cohomology theory for Lusztig's graded affine Hecke algebras. We apply these constructions to the case of symplectic reflection algebras defined by Etingof-Ginzburg, particularly to rational Cherednik algebras for real or complex reflection groups with parameters t,c. ...”

Representation Theory in Complex Rank, I di Etingof, Pavel I.

“...Generalizing these results, we propose a method of interpolating representation categories of various algebras containing S [subscript n] (such as degenerate affine Hecke algebras, symplectic reflection algebras, rational Cherednik algebras, etc.) to complex values of n. ...”
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Cherednik and Hecke Algebras of Varieties with a Finite Group Action di Etingof, Pavel I

“...This includes usual, affine, and double affine Hecke algebras for Weyl groups, Hecke algebras of complex reflection groups, as well as many new examples. ...”
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